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Simplifying 4x2 + 10x + 3 = 0 Reorder the terms: 3 + 10x + 4x2 = 0 Solving 3 + 10x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 2.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 2.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 2.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 2.5x + x2 = 0 + -0.75 2.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 2.5x + x2 = -0.75 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -0.75 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -0.75 + 1.5625 Combine like terms: -0.75 + 1.5625 = 0.8125 1.5625 + 2.5x + x2 = 0.8125 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (x + 1.25) equal to 0.901387819 and -0.901387819.Subproblem 1
x + 1.25 = 0.901387819 Simplifying x + 1.25 = 0.901387819 Reorder the terms: 1.25 + x = 0.901387819 Solving 1.25 + x = 0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 0.901387819 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 0.901387819 + -1.25 x = 0.901387819 + -1.25 Combine like terms: 0.901387819 + -1.25 = -0.348612181 x = -0.348612181 Simplifying x = -0.348612181Subproblem 2
x + 1.25 = -0.901387819 Simplifying x + 1.25 = -0.901387819 Reorder the terms: 1.25 + x = -0.901387819 Solving 1.25 + x = -0.901387819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -0.901387819 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -0.901387819 + -1.25 x = -0.901387819 + -1.25 Combine like terms: -0.901387819 + -1.25 = -2.151387819 x = -2.151387819 Simplifying x = -2.151387819Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.348612181, -2.151387819}
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